Existence and uniqueness of solutions for two- dimensional fractional non- colliding particle systems
Email:
vthuong@utc.edu.vn
Từ khóa:
Stochastic differential equation, fractional Brownian motion, non- colliding particle systems.
Tóm tắt
In this paper, we consider the stochastic evolution of two particles with electrostatic repulsion and restoring force which is modeled by a system of stochastic differential equations driven by fractional Brownian motion where the diffusion coefficients are constant. This is the simplest case for some classes of non- colliding particle systems such as Dyson Brownian motions, Brownian particles systems with nearest neighbour repulsion. We will prove that the equation has a unique non- colliding solution in path- wise sense.Tài liệu tham khảo
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[10] Y.. Mishura, A. Yurchenko-Tytarenko, Fractional Cox-Ingersoll-Ross process with non-zero “mean”, Modern Stochastic: Theory and Applications, 5 (2018) 99-111. https://doi.org/10.15559/18-VMSTA97
[2] M. Katori, H. Tanemura, Noncolliding Squared Bessel processes, J. Stat. Phys., 142 (2011) 592-615. https://doi.org/10.1007/s10955-011-0117-y
[3] M. Katori, H. Tanemura, Noncolliding processes, matrix-valued processes and determinantal processes, Sugaku Expositions, 24 (2011) 263-289. https://doi.org/10.11429/sugaku.0613225
[4] E. Cepa, D. Lepingle, Diffusing particles with electrostatic repulsion, Probab.Theory Related Fields, 107 (1997) 429-449. https://doi.org/10.1007/s004400050092
[5] P. Graczyk, J. Ma lecki, Strong solutions of non-colliding particle systems, Electron. J. Probab, 19(2014) 1-21.
[6] L. C. G. Rogers, Z. Shi, Interacting Brownian particles and the Wigner law, Probab. Theory Related Fields, 95 (1993) 555-570. https://doi.org/10.1007/BF01196734
[7] N. Naganuma, D. Taguchi, Malliavin Calculus for Non-colliding Particle Systems, Stochastic Processes and their Applications, 2019. https://doi.org/10.1016/j.spa.2019.07.005
[8] D. Nualart, A. Rascanu, Differential equations driven by fractional Brownian motion, Collectanea Mathematica, 53 (2002) 177-193.
[9] Y. S. Mishura, Stochastic Calculus for Fractional Brownian Motion and Related Processes, Lecture Notes in Math, Springer, Berlin, 2008.
[10] Y.. Mishura, A. Yurchenko-Tytarenko, Fractional Cox-Ingersoll-Ross process with non-zero “mean”, Modern Stochastic: Theory and Applications, 5 (2018) 99-111. https://doi.org/10.15559/18-VMSTA97
Tải xuống
Chưa có dữ liệu thống kê
Nhận bài
05/11/2019
Nhận bài sửa
02/12/2019
Chấp nhận đăng
05/12/2019
Xuất bản
31/01/2020
Chuyên mục
Công trình khoa học
Kiểu trích dẫn
Vu Thi, H. (1580403600). Existence and uniqueness of solutions for two- dimensional fractional non- colliding particle systems. Tạp Chí Khoa Học Giao Thông Vận Tải, 71(1), 11-17. https://doi.org/10.25073/tcsj.71.1.2
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